@book{shtesselSlidingModeControl2014,
  title = {Sliding Mode Control and Observation},
  author = {Shtessel, Yuri and Edwards, Christopher and Fridman, Leonid and Levant, Arie},
  year = {2014},
  series = {Control {{Engineering}}},
  publisher = {{Springer New York}},
  address = {{New York, NY}},
  doi = {10.1007/978-0-8176-4893-0},
  urldate = {2023-12-27},
  isbn = {978-0-8176-4892-3 978-0-8176-4893-0},
  langid = {english},
  file = {C:\Users\jinze\Zotero\storage\J6RF6BG6\Shtessel 等 - 2014 - Sliding Mode Control and Observation.pdf}
}
@article{SEEBER2017241,
title = {Stability proof for a well-established super-twisting parameter setting},
journal = {Automatica},
volume = {84},
pages = {241-243},
year = {2017},
issn = {0005-1098},
doi = {https://doi.org/10.1016/j.automatica.2017.07.002},
url = {https://www.sciencedirect.com/science/article/pii/S000510981730328X},
author = {Richard Seeber and Martin Horn},
keywords = {Sliding mode control, Super-twisting algorithm, Stability proof, Lyapunov function},
abstract = {Several sufficient stability conditions exist for the super-twisting algorithm. For its tuning in practical applications, however, a popular parameter set is regularly used, which is provided in literature without any stability proof. This short note provides a novel, simple sufficient stability condition which includes this very popular parameter setting.}
}
@article{xianContinuousAsymptoticTracking2004,
  title = {A Continuous Asymptotic Tracking Control Strategy for Uncertain Nonlinear Systems},
  author = {Xian, B. and Dawson, D.M. and {deQueiroz}, M.S. and Chen, J.},
  year = {2004},
  month = jul,
  journal = {IEEE Transactions on Automatic Control},
  volume = {49},
  number = {7},
  pages = {1206--1206},
  issn = {0018-9286},
  doi = {10.1109/TAC.2004.831148},
  urldate = {2024-01-25},
  abstract = {In this note, we present a new continuous control mechanism that compensates for uncertainty in a class of high-order, multiple-input{\textendash}multiple-output nonlinear systems. The control strategy is based on limited assumptions on the structure of the system nonlinearities. A new Lyapunov-based stability argument is employed to prove semiglobal asymptotic tracking.},
  langid = {english},
  file = {C:\Users\jinze\Zotero\storage\DR94FBNA\Xian 等 - 2004 - A continuous asymptotic tracking control strategy for uncertain nonlinear systems.pdf}
}


@article{songPrescribedtimeControlIts2023,
  title = {Prescribed-Time Control and Its Latest Developments},
  author = {Song, Yongduan and Ye, Hefu and Lewis, Frank L.},
  date = {2023},
  journaltitle = {IEEE Transactions on Systems, Man, and Cybernetics: Systems},
  shortjournal = {IEEE Trans. Syst. Man Cybern.: Syst.},
  pages = {1--15},
  issn = {2168-2216, 2168-2232},
  doi = {10.1109/TSMC.2023.3240751},
  url = {https://ieeexplore.ieee.org/document/10044666/},
  urldate = {2023-06-02},
  abstract = {Prescribed-time (PT) control for nonlinear systems, originated from Song et al., has gained increasing attention among the control community. The salient feature of PT con突出的 trol lies in its ability to achieve system stability within a finite settling time user-assignable in advance irrespective of initial conditions. It is such a unique feature that has enticed many follow-up studies on this technically important area, motivating numerous research advancements. In this article, we provide a comprehensive survey on the recent developments in PT control. Through a concise introduction to the concept of PT control, and a unique taxonomy covering: 1) from robust PT control to adaptive PT control; 2) from PT control for single-input–single-output (SISO) systems to multi-input–multioutput (MIMO) systems; and 3) from PT control for an isolated system to multiagent systems, we present an accessible review of this interesting topic. We highlight key techniques, and fundamental assumptions adopted in various developments as well as some new design ideas. We also discuss several possible future research directions toward PT control.},
  langid = {english},
  keywords = {综述},
  file = {C\:\\Users\\jinze\\Zotero\\storage\\BFFYRZBW\\Song 等 - 2023 - Prescribed-Time Control and Its Latest Development.pdf;C\:\\Users\\jinze\\Zotero\\storage\\K84DLXKF\\Ye 等 - 2022 - Prescribed-Time Control and Its Latest Development.pdf}
}

@book{brogliatoNonsmoothMechanicsModels2016,
  title = {Nonsmooth {{Mechanics}}: {{Models}}, {{Dynamics}} and {{Control}}},
  shorttitle = {Nonsmooth {{Mechanics}}},
  author = {Brogliato, Bernard},
  year = {2016},
  series = {Communications and {{Control Engineering}}},
  publisher = {Springer International Publishing},
  address = {Cham},
  doi = {10.1007/978-3-319-28664-8},
  urldate = {2024-01-22},
  isbn = {978-3-319-28662-4 978-3-319-28664-8},
  langid = {english},
  keywords = {Complementarity Problems and Systems,Convex Analysis and Complementarity Theory,Hybrid Dynamical Systems,Impact and Contact Mechanics,Impulsive Systems,Mechanical Systems with Constraints,Moreau's Sweeping Process and Variational Inequalities,Multibody Multicontact Mechanical Systems,Stability and Control of Non-smooth Lagrangian Systems,Unilateral & Bilateral Constraints with or,without Coulomb's Friction},
  file = {C:\Users\jinze\Zotero\storage\RJ7HRSWV\Brogliato - 2016 - Nonsmooth Mechanics Models, Dynamics and Control.pdf}
}

@article{cortesDiscontinuousDynamicalSystems2008,
  title = {Discontinuous Dynamical Systems},
  author = {Cortes, Jorge},
  year = {2008},
  month = jun,
  journal = {IEEE Control Systems Magazine},
  volume = {28},
  number = {3},
  pages = {36--73},
  issn = {1941-000X},
  doi = {10.1109/MCS.2008.919306},
  urldate = {2023-12-11},
  abstract = {This article has presented an introductory tutorial on discontinuous dynamical systems. Various examples illustrate the pertinence of the continuity and Lipschitzness properties that guarantee the existence and uniqueness of classical solutions to ordinary differential equations. The lack of these properties in examples drawn from various disciplines motivates the need for more general notions than the classical one. First, we introduced notions of solution for discontinuous systems. Second, we reviewed the available tools from non- smooth analysis to study the gradient information of candidate Lyapunov functions. And, third, we presented nonsmooth stability tools to characterize the asymptotic behavior of solutions.},
  langid = {american},
  file = {C:\Users\jinze\Zotero\storage\N6N5VYUJ\Cortes - 2008 - Discontinuous dynamical systems.pdf}
}

@book{hanTheoryControlSystems2016,
  title = {Theory of Control Systems Described by Differential Inclusions},
  author = {Han, Zhengzhi and Cai, Xiushan and Huang, Jun},
  year = {2016},
  series = {Springer {{Tracts}} in {{Mechanical Engineering}}},
  publisher = {Springer Berlin Heidelberg},
  address = {Berlin, Heidelberg},
  doi = {10.1007/978-3-662-49245-1},
  urldate = {2023-12-17},
  isbn = {978-3-662-49243-7 978-3-662-49245-1},
  langid = {american},
  file = {C:\Users\jinze\Zotero\storage\2UVKM2QW\Han 等 - 2016 - Theory of Control Systems Described by Differential Inclusions.pdf}
}

@book{orlovAdvancedControlNonsmooth2014,
  title = {Advanced {{H}}{$\infty$} {{Control}}: {{Towards Nonsmooth Theory}} and {{Applications}}},
  shorttitle = {Advanced {{H}}{$\infty$} {{Control}}},
  author = {Orlov, Yury V. and Aguilar, Luis T.},
  year = {2014},
  series = {Systems \& {{Control}}: {{Foundations}} \& {{Applications}}},
  publisher = {Springer},
  address = {New York, NY},
  doi = {10.1007/978-1-4939-0292-7},
  urldate = {2024-01-22},
  isbn = {978-1-4939-0291-0 978-1-4939-0292-7},
  langid = {english},
  keywords = {backstepping approach,disturbance attenuation,H-infinity,Lyapunov function,nonsmooth analysis and systems,partial differential equations,robust H-infinity and sliding mode control,underactuated system},
  file = {C:\Users\jinze\Zotero\storage\X49EW83Y\Orlov和Aguilar - 2014 - Advanced H∞ Control Towards Nonsmooth Theory and Applications.pdf}
}

#part 2
@book{polyakov_generalized_2020,
	address = {Cham},
	series = {Communications and {Control} {Engineering}},
	title = {Generalized homogeneity in systems and control},
	isbn = {978-3-030-38448-7 978-3-030-38449-4},
	url = {http://link.springer.com/10.1007/978-3-030-38449-4},
	language = {en},
	urldate = {2024-01-18},
	publisher = {Springer International Publishing},
	author = {Polyakov, Andrey},
	year = {2020},
	doi = {10.1007/978-3-030-38449-4},
	file = {Polyakov - 2020 - Generalized Homogeneity in Systems and Control.pdf:/Users/apple/Zotero/storage/3HKSXT6Z/Polyakov - 2020 - Generalized Homogeneity in Systems and Control.pdf:application/pdf},
}

@phdthesis{马诺诺2010齐次性理论在非线性系统稳定性分析及控制设计中的应用,
	address = {济南},
	type = {phd},
	title = {齐次性理论在非线性系统稳定性分析及控制设计中的应用},
	language = {zh},
	school = {山东大学},
	author = {{马诺诺}},
	year = {2010},
	keywords = {齐次性},
	file = {马诺诺 - 2010 - 齐次性理论在非线性系统稳定性分析及控制设计中的应用.pdf:/Users/apple/Zotero/storage/ZJETK3KC/马诺诺 - 2010 - 齐次性理论在非线性系统稳定性分析及控制设计中的应用.pdf:application/pdf},
}

@misc{Utkin2017,
  title = {Sliding Mode Control in Electro-Mechanical Systems},
  ISBN = {9781315218977},
  url = {http://dx.doi.org/10.1201/9781420065619},
  DOI = {10.1201/9781420065619},
  publisher = {CRC Press},
  author = {Utkin,  Vadim and Guldner,  J\"{u}rgen and Shi,  Jingxin},
  year = {2017},
  month = dec 
}


@article{moreno_strict_2012,
	title = {Strict lyapunov functions for the super-twisting algorithm},
	volume = {57},
	issn = {1558-2523},
	url = {https://ieeexplore.ieee.org/document/6144710},
	doi = {10.1109/TAC.2012.2186179},
	abstract = {A method to construct a family of strict Lyapunov functions, i.e., with negative definite derivative, for the super-twisting algorithm, without or with perturbations, is provided. This second order sliding modes algorithm is widely used to design controllers, observers and exact differentiators. The proposed Lyapunov functions ascertain finite time convergence, provide an estimate of the convergence time, and ensure the robustness of the finite-time or ultimate boundedness for a class of perturbations wider than the classical ones for this algorithm. Since the Lyapunov functions and their derivatives are quadratic forms, the operation with them is as simple as for linear time invariant systems.},
	language = {en},
	number = {4},
	urldate = {2024-01-26},
	journal = {IEEE Transactions on Automatic Control},
	author = {Moreno, Jaime A. and Osorio, Marisol},
	month = apr,
	year = {2012},
	note = {Conference Name: IEEE Transactions on Automatic Control},
	keywords = {Lyapunov methods},
	pages = {1035--1040},
	file = {IEEE Xplore Full Text PDF:C\:\\Users\\jinze\\Zotero\\storage\\F5RM8GBW\\Moreno和Osorio - 2012 - Strict Lyapunov Functions for the Super-Twisting Algorithm.pdf:application/pdf},
}

@article{colotti_new_2022,
	title = {New convergence conditions for the super twisting algorithm with uncertain input gain},
	volume = {143},
	issn = {00051098},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0005109822002771},
	doi = {10.1016/j.automatica.2022.110423},
	abstract = {A simple proof is proposed that extends Seeber and Horn’s recent sufficient conditions (Seeber and Horn, 2017) for the finite time convergence of the super twisting algorithm to perturbations in the input gain. The new convergence conditions are compared to state of the art conditions, and turn out to accept sensibly smaller gains.},
	language = {en},
	urldate = {2024-01-25},
	journal = {Automatica},
	author = {Colotti, Alessandro and Monnet, Dominique and Goldsztejn, Alexandre and Plestan, Franck},
	month = sep,
	year = {2022},
	keywords = {稳定性分析},
	pages = {110423},
	file = {Colotti 等 - 2022 - New convergence conditions for the super twisting algorithm with uncertain input gain.pdf:C\:\\Users\\jinze\\Zotero\\storage\\ADKK8IMA\\Colotti 等 - 2022 - New convergence conditions for the super twisting algorithm with uncertain input gain.pdf:application/pdf},
}

@article{levant_principles_2007,
	title = {Principles of 2-sliding mode design},
	volume = {43},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {00051098},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0005109806004432},
	doi = {10.1016/j.automatica.2006.10.008},
	abstract = {Second-order sliding modes are used to keep exactly a constraint of the second relative degree or just to avoid chattering, i.e. in the cases when the standard (ﬁrst order) sliding mode implementation might be involved or impossible. Design of a number of new 2-sliding controllers is demonstrated by means of the proposed homogeneity-based approach. A recently developed robust exact differentiator being applied, robust output-feedback controllers with ﬁnite-time convergence are produced, capable to control any general uncertain single-input–single-output process with relative degree 2. An effective simple procedure is developed to attenuate the 1-sliding mode chattering. Simulation of new controllers is presented.},
	language = {en},
	number = {4},
	urldate = {2024-04-11},
	journal = {Automatica},
	author = {Levant, Arie},
	month = apr,
	year = {2007},
	pages = {576--586},
	file = {Levant - 2007 - Principles of 2-sliding mode design.pdf:C\:\\Users\\jinze\\Zotero\\storage\\8B6VJYFD\\Levant - 2007 - Principles of 2-sliding mode design.pdf:application/pdf},
}

@article{seeber_stability_2017,
	title = {Stability proof for a well-established super-twisting parameter setting},
	volume = {84},
	issn = {00051098},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S000510981730328X},
	doi = {10.1016/j.automatica.2017.07.002},
	abstract = {Several sufficient stability conditions exist for the super-twisting algorithm. For its tuning in practical applications, however, a popular parameter set is regularly used, which is provided in literature without any stability proof. This short note provides a novel, simple sufficient stability condition which includes this very popular parameter setting.},
	language = {en},
	urldate = {2024-01-25},
	journal = {Automatica},
	author = {Seeber, Richard and Horn, Martin},
	month = oct,
	year = {2017},
	keywords = {稳定性分析, Lyapunov methods},
	pages = {241--243},
	file = {Seeber和Horn - 2017 - Stability proof for a well-established super-twisting parameter setting.pdf:C\:\\Users\\jinze\\Zotero\\storage\\BC3ELDAL\\Seeber和Horn - 2017 - Stability proof for a well-established super-twisting parameter setting.pdf:application/pdf},
}

@article{levant_homogeneity_2005,
	title = {Homogeneity approach to high-order sliding mode design},
	volume = {41},
	copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
	issn = {00051098},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0005109805000142},
	doi = {10.1016/j.automatica.2004.11.029},
	abstract = {It is shown that a general uncertain single-input–single-output regulation problem is solvable only by means of discontinuous control laws, giving rise to the so-called high-order sliding modes. The homogeneity properties of the corresponding controllers yield a number of practically important features. In particular, ﬁnite-time convergence is proved, and asymptotic accuracy is calculated in a very general way in the presence of input noises, discrete measurements and switching delays. A robust homogeneous differentiator is included in the control structure thus yielding robust output-feedback controllers with ﬁnite-time convergence. It is demonstrated that homogeneity features signiﬁcantly simplify the design and investigation of a new family of high-order sliding-mode controllers. Finally, simulation results are presented.},
	language = {en},
	number = {5},
	urldate = {2024-04-11},
	journal = {Automatica},
	author = {Levant, Arie},
	month = may,
	year = {2005},
	pages = {823--830},
	file = {Levant - 2005 - Homogeneity approach to high-order sliding mode design.pdf:C\:\\Users\\jinze\\Zotero\\storage\\9C7CJZ67\\Levant - 2005 - Homogeneity approach to high-order sliding mode design.pdf:application/pdf},
}

@article{orlov_finite_2004,
	title = {Finite time stability and robust control synthesis of uncertain switched systems},
	volume = {43},
	issn = {0363-0129, 1095-7138},
	url = {http://epubs.siam.org/doi/10.1137/S0363012903425593},
	doi = {10.1137/S0363012903425593},
	abstract = {Stability analysis is developed for uncertain nonlinear switched systems. While being asymptotically stable and homogeneous of degree q {\textless} 0, these systems are shown to approach the equilibrium point in ﬁnite time. Restricted to second order systems, this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations. Based on this fundamental property, switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m-vector relative degree (2, . . . , 2)T . The controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. The proposed synthesis procedure is illustrated via application to a friction servo-motor.},
	language = {en},
	number = {4},
	urldate = {2024-04-11},
	journal = {SIAM Journal on Control and Optimization},
	author = {Orlov, Y.},
	month = jan,
	year = {2004},
	pages = {1253--1271},
	file = {Orlov - 2004 - Finite time stability and robust control synthesis of uncertain switched systems.pdf:C\:\\Users\\jinze\\Zotero\\storage\\5E8DWH8V\\Orlov - 2004 - Finite time stability and robust control synthesis of uncertain switched systems.pdf:application/pdf},
}

@article{polyakov_reaching_2009,
	title = {Reaching time estimation for “super-twisting” second order sliding mode controller via lyapunov function designing},
	volume = {54},
	copyright = {https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html},
	issn = {0018-9286, 1558-2523},
	url = {http://ieeexplore.ieee.org/document/5173492/},
	doi = {10.1109/TAC.2009.2023781},
	abstract = {A method of a Lyapunov functions design based on resolving of the ﬁrst-order partial differential equation of a special type is presented. A successful resolution of this equation guaranties a ﬁnite-time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right-hand side. It is also provides an analytical formula for an upper bound of the corresponding reaching time. The suggested method is applied to the problem of a stability analysis and a reaching time estimation of the, so-called, “super-twisting” controller. The estimation accuracy is conﬁrmed by numerical example.},
	language = {en},
	number = {8},
	urldate = {2024-04-11},
	journal = {IEEE Transactions on Automatic Control},
	author = {Polyakov, A. and Poznyak, A.},
	month = aug,
	year = {2009},
	pages = {1951--1955},
	file = {Polyakov和Poznyak - 2009 - Reaching time estimation for “super-twisting” second order sliding mode controller via lyapunov func.pdf:C\:\\Users\\jinze\\Zotero\\storage\\VZBBG96M\\Polyakov和Poznyak - 2009 - Reaching time estimation for “super-twisting” second order sliding mode controller via lyapunov func.pdf:application/pdf},
}
